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Two contractors are competing for a sequence of contracts to provide the government with military supplies. Each month there is a new contract put out for bids for the two contractors. The cost to a contractor for providing the supplies a given month is a positive integer C, and the cost is the same for both contractors and the same in all months. The contractors can submit costs to the government in a given month that are nonnegative integers, with a maximum bid of M > C+4. Thus, their bids must be a nonnegative integer in {0,1,2,3,...,M}. The government picks the contractor with the lowest cost in order to provide the supplies in a given month, flipping a fair coin if the bids are tied.

The contractors arrange to collude, agreeing that contractor 1 will bid M-1 and contractor 2 will bid M in odd months, so that contractor 1 will win the contract in odd months, and then they will reverse these in even months so that contractor 1 will bid M and contractor 2 will bid M-1 in even months, so that contractor 2 will win the contract in even months. The contractors agree to enforce this via a grim-trigger strategy of simply both bidding C forever after if the agreement is broken.

a. If a contractor decides to deviate from this agreement, what would the optimal deviation be?b. Suppose that M = 10 and C = 1. For which values of "delta" is this a subgame perfect equilibrium of the infinitely repeated game?

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